### Silhouette Island

Quick experiment with marching cubes using the mountains from Contour Lines Island

// LL 2021

const turtle = new Turtle();

const detail = 0.0;        /// min=0 max=1 step=0.1
const perspective = 2;     /// min=1 max=3 step=0.1
const camera_theta = 0.3;  // min=-1 max=1 step=0.01
const camera_phi = 0.3;    // min=-0.99 max=1 step=0.01
const camera_r = 28;       // min=0.1 max=40 step=0.1
const look_at_z = 9;       // min=-100 max=100 step=0.1
const inside_lines = 0.45; // min=0 max=1 step=0.01
const style = 2;           // min=0 max=3 step=1 (Preview,All outlines,Silhouette,Hatched)
const render = 1;          // min=0 max=1 step=1 (Voxels,Marching cubes)
const seed = 0;            // min=0 max=100 step=1

const detail_max_length = Math.max(0.9, 0.9 + 5 * (1 - detail));

var silhouette = new Silhouette();

const noise = SimplexNoise(seed ? seed : Math.floor(Math.random() * 1000));

function walk(i, t) {
if (i==0) {
if (t == 0 || t == 1) initOnce();
initFrame(t);
}

if (silhouette.faceCount() < 1) {
// for (var y = -100; y <= 100; y += 1) {
//         const p1 = polygons.create();
//         const dpoints = [];
//         const sx = Math.cos(y/55) * 70 + random() * 50;
//         for (var x=-sx; x<=sx; x += 1) {
//             const wy = Math.abs(Math.sin(y/4+x/2)) * 2 + y;
//             dpoints.push([x, wy]);
//             dpoints.unshift([x, wy]);
//         }
//         polygons.draw(turtle, p1, false);
// }
return false;
}

silhouette.nextFace().draw();

return true;
}

function initFrame(t) {
const cameraOffset = [
camera_r * perspective ** 3 * Math.cos((camera_theta+t*2) * Math.PI) * Math.sin((camera_phi/2+0.5) * Math.PI),
camera_r * perspective ** 3 * Math.sin((camera_theta+t*2) * Math.PI) * Math.sin((camera_phi/2+0.5) * Math.PI),
-camera_r * perspective ** 3 * Math.cos((camera_phi/2+0.5) * Math.PI)
];
const cameraLookAt = [0, 0, look_at_z];

polygons = new Polygons();

silhouette.processFrameModels();
silhouette.sortFaces();
}

function initOnce(t) {
seed_t = (t < 1 && seed == 0) ? (Math.random() * 100 | 0) : seed;
rng = undefined;

initScene();

silhouette.processOnceModels();
}

function initScene() {
const count = 128;
const mdl = makeMountains(count);
var matrix = new Matrix();
matrix.translate(0, count/2, 0);
matrix.scale(128/count);
mdl.transform(matrix);
}

/////////////////////////////////////////////////////////////////////
// Prototype Silhouette utility code - Created by Lionel Lemarie 2021
// https://turtletoy.net/turtle/334500a2c5

function Silhouette() {
const models = [];
const all_faces = [];

class Model {
constructor() {
this.faces = [];
this.edges = [];
this.hide_overlap = true;
}

transform(matrix) {
this.faces.forEach(face => {
face.transform(matrix);
});
}

processOnce() {
if (detail && style) this.subdivideDetail(detail_max_length);
this.updateEdgeList();
}

processFrame() {
this.findStaticOutlines();
this.findProjectedOutlines();
}

this.edges.forEach(edge => {
edge.faces.forEach(face => {
const pc = face.points.length;
if (pc > 1) {
for (var i=0; i<pc; i++) {
const hash0 = getPointHash(face.points[i]);
const hash1 = getPointHash(face.points[(i+1)%pc]);
if (edge.hash == hash0 + hash1 || edge.hash == hash1 + hash0) {
if (edge.state) {
} else {
}
}
}
}
});
});
}

const face = new Face(points);
this.faces.push(face);
}

merge(model) {
model.faces.forEach(face => { this.faces.push(face); })
}

subdivideDetail(max_length) {
var nfaces = this.faces.length;
var loop = true;
while (loop) {
const old_faces = this.faces;
this.faces = [];
old_faces.forEach(face => {
const new_faces = face.getSubdivided(max_length);
this.faces = [...this.faces, ...new_faces];
});
loop = this.faces.length != nfaces;
nfaces = this.faces.length;
}
}

subdivideCount(count) {
while (count-- > 0) {
const old_faces = this.faces;
this.faces = [];
old_faces.forEach(face => {
const new_faces = face.getSubdivided(0);
this.faces = [...this.faces, ...new_faces];
});
}
}

updateEdgeList() {
this.edges = [];
const edge_lookup = {};
this.faces.forEach(face => {
const pc = face.points.length;
if (pc > 1) {
for (var i=0; i<pc; i++) {
const hash0 = getPointHash(face.points[i]);
const hash1 = getPointHash(face.points[(i+1)%pc]);
if ((hash0 + hash1) in edge_lookup) {
const edge_id = edge_lookup[hash0 + hash1];
} else if ((hash1 + hash0) in edge_lookup) {
const edge_id = edge_lookup[hash1 + hash0];
} else {
const edge_id = this.edges.length;
edge_lookup[hash0 + hash1] = edge_id;
this.edges.push({ faces: [face], hash: hash0 + hash1, state: 1 });
}
}
}
});
}

var good = true;
this.edges[edge_id].faces.forEach(face => {
if (face.matches(new_face)) {
good = false;
if (this.hide_overlap) face.overlap = true;
new_face.overlap = true;
}
});
if (good) this.edges[edge_id].faces.push(new_face);
}

findStaticOutlines() {
this.edges.forEach(edge => {
edge.state = 1;
for (var i=0, fl=edge.faces.length; i<fl && edge.state; i++) {
if (edge.faces[i].overlap) continue;
const nfi = edge.faces[i].getStaticNormal();
for (var j=i+1; j<fl && edge.state; j++) {
if (edge.faces[j].overlap) continue;
const nfj = edge.faces[j].getStaticNormal();
const d = len3(sub3(nfi, nfj));
if (d < inside_lines * 2) { edge.state = 0; }
}
}
});
}

findProjectedOutlines() {
this.edges.forEach(edge => {
var found_pos = false, found_neg = false;
edge.faces.forEach(face => {
if (!face.overlap) {
const nf = face.getProjectedNormal();
const EPS = 0.001;
if (nf[2] <   EPS) found_neg = true;
if (nf[2] >= -EPS) found_pos = true;
}
});
if (found_pos && found_neg) edge.state = 1;
});
}
}

function getPointHash(point) {
const mult = 100;
const x0 = Math.round(point[0] * mult), y0 = Math.round(point[1] * mult), z0 = Math.round(point[2] * mult);
return `\${x0},\${y0},\${z0}`;
}

class Face {
constructor(points) {
this.points = [...points];
this.z = 0;
this.projected_points = [];
this.overlap = false;
}

draw() {
if (this.projected_points.length < 2 || this.overlap) return;

var good = true;
this.projected_points.forEach(p => good &= Math.min(Math.abs(p[0]), Math.abs(p[1])) < 100 );
if (!good) return;

if (style == 0) {
// turtle.jump(this.projected_points[this.projected_points.length-1]);
// this.projected_points.forEach(p=>turtle.goto(p));
for (var i=0; i<this.projected_points.length; i++) {
if (this.outline_mask & (1 << i)) {
turtle.jump(this.projected_points[i]);
turtle.goto(this.projected_points[(i+1) % this.projected_points.length]);
}
}
} else {
const p1 = polygons.create();
if (style == 1) {
} else if (style > 1) {
for (var i=0; i<this.projected_points.length; i++) {
if (this.outline_mask & (1 << i)) {
}
}
if (style > 2) {
const hmin = 0.15, hmax = 0.9;
const hatching = hmin + (hmax - hmin) * this.getLight();
}
}
polygons.draw(turtle, p1, true);
}
}

getStaticNormal() {
if (this.cached_static_normal === undefined) {
if (this.points.length < 3) this.cached_static_normal = [0, 1, 0];
else this.cached_static_normal = normalize3(cross3(sub3(this.points[1], this.points[0]), sub3(this.points[2], this.points[0])));
}
return this.cached_static_normal;
}

getProjectedNormal() {
if (this.projected_points.length < 3) return [0, 1, 0];
return normalize3(cross3(sub3(this.projected_points[1], this.projected_points[0]), sub3(this.projected_points[2], this.projected_points[0])));
}

getLight() {
const n = this.getProjectedNormal();
return n[0] * 0.5 + 0.5;
}

transform(matrix) {
for (var i=0, c=this.points.length; i<c; i++) {
this.points[i] = matrix.transform(this.points[i]);
}
}

if (this.overlap) return;

this.projected_points = [];
this.z = 0;
this.points.forEach(point => {
const pp = project(point);
if (pp === undefined) return;
this.projected_points.push(pp);
this.z += pp[2];
})
if (this.projected_points.length > 0) this.z /= this.projected_points.length;

}

getSubdivided(max_length) {
var long_index = -1;
const pc = this.points.length;

for (var i=0; i<pc; i++) {
const len = len3(sub3(this.points[(i+1)%pc],this.points[i]));
if (len > max_length) {
max_length = len;
long_index = i;
}
}

if (long_index >= 0) {
if (pc == 4) {
const new_faces = [];
new_faces.push(new Face([this.points[0], this.points[1], this.points[2]]));
new_faces.push(new Face([this.points[2], this.points[3], this.points[0]]));
return new_faces;
} else {
const new_faces = [];
for (var i=0; i<pc; i++) {
if (i != long_index) {
new_faces.push(new Face([this.points[i], this.points[(i+1)%pc], point]));
}
}
return new_faces;
}
}
return [ this ];
}

matches(face) {
const fl = face.points.length;
if (fl != this.points.length) return false;
if (fl < 1) return true;

var first_id = undefined;
{
const hash0 = getPointHash(this.points[0]);
for (var i=0; i<fl; i++) {
const hash1 = getPointHash(face.points[i]);
if (hash0 == hash1) { first_id = i; break; }
}
}
if (first_id === undefined) return false;

for (var i=1; i<fl; i++) {
const j = (first_id - i + fl) % fl;
const hash0 = getPointHash(this.points[i]);
const hash1 = getPointHash(face.points[j]);
if (hash0 != hash1) {
for (var i2=1; i2<fl; i2++) {
const j2 = (first_id + i2) % fl;
const hash0 = getPointHash(this.points[i2]);
const hash1 = getPointHash(face.points[j2]);
if (hash0 != hash1) return false;
}
return true;
}
}
return true;
}
}

return {
addModel: (model) => { models.push(model); },
newModel: () => { return new Model(); },
processFrameModels: () => { models.forEach(model => { model.processFrame(); }); },
processOnceModels: () => { models.forEach(model => { model.processOnce(); }); },
modelCount: () => { return models.length; },
sortFaces: () => { all_faces.sort(function(a, b) { return a.z - b.z; }); },
nextFace: () => { return all_faces.shift(); },
faceCount: () => { return all_faces.length; },
addFace: (face) => { all_faces.push(face); },
};
}

class Matrix {
constructor() { this.identity(); }

identity() {
this.matrix = [ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ];
return this;
}

translate(tx, ty, tz) {
const m2 = new Matrix();
m2.matrix[12] = tx;
m2.matrix[13] = ty;
m2.matrix[14] = tz;
return this.multiply(m2);
}

scale(sx, sy, sz) {
if (sy === undefined) sy = sx;
if (sz === undefined) sz = sy;
const m2 = new Matrix();
m2.matrix[0]  *= sx;
m2.matrix[5]  *= sy;
m2.matrix[10] *= sz;
return this.multiply(m2);
}

rotateX(a) {
const m2 = new Matrix();
m2.matrix[5]  =  Math.cos(a);
m2.matrix[9]  =  Math.sin(a);
m2.matrix[6]  = -Math.sin(a);
m2.matrix[10] =  Math.cos(a);
return this.multiply(m2);
}

rotateY(a) {
const m2 = new Matrix();
m2.matrix[0]  =  Math.cos(a);
m2.matrix[8]  = -Math.sin(a);
m2.matrix[2]  =  Math.sin(a);
m2.matrix[10] =  Math.cos(a);
return this.multiply(m2);
}

rotateZ(a) {
const m2 = new Matrix();
m2.matrix[0]  =  Math.cos(a);
m2.matrix[1]  = -Math.sin(a);
m2.matrix[4]  =  Math.sin(a);
m2.matrix[5]  =  Math.cos(a);
return this.multiply(m2);
}

multiply(rhs) {
const m1 = [...this.matrix];
const m2 = [...rhs.matrix];
this.matrix = [];
for(let n=0; 16>n; n+=4) {
for(let o=0; 4>o; o++) {
this.matrix[n+o] = m1[n+0] * m2[0+o] + m1[n+1] * m2[4+o] + m1[n+2] * m2[8+o] + m1[n+3] * m2[12+o];
}
}
return this;
}

transform(point) {
const p = [...point];
for (let i=0; i<3; i++) {
p[i] = this.matrix[i] * point[0] + this.matrix[i+4] * point[1] + this.matrix[i+8] * point[2] + this.matrix[i+12];
}
return p;
}
}

const cube_points = [];
for (var z=-1; z<=1; z+=2) { for (var y=-1; y<=1; y+=2) { for (var x=-1; x<=1; x+=2) { cube_points.push([x, y, z]); } } }
const cube_faces = [ [0, 1, 2, 3], [7, 3, 5, 1], [6, 2, 7, 3], [0, 4, 1, 5], [4, 0, 6, 2], [6, 7, 4, 5] ];

function makeBox(w, h, d) {
const model = silhouette.newModel();

cube_faces.forEach(f => {
const quad = [ [...cube_points[f[0]]], [...cube_points[f[1]]], [...cube_points[f[3]]], [...cube_points[f[2]]] ];
quad.forEach(point => { point[0] *= w/2; point[1] *= h/2; point[2] *= d/2; });
});

return model;
}

function heightField(p) {
let x = p[0]/60, y = p[1]/60;
let height = noise.noise2D([x,y]);
height += .55 * noise.noise2D([x*2+3.4,y*2-56.1]);
height += .35 * Math.abs(1-noise.noise2D([x*4+21.2,y*4+.5]));
height += .25 * Math.abs(1-noise.noise2D([x*8+421.12,y*8+21.3]));
// 	height += .15 * Math.abs(1-noise.noise2D([x*32+150.34,y*32+150.34]));
height += 1 - 2.5 * ((p[0]/100)**2 + (p[1]/100)**2);
height = Math.max(height, 0) ** 2;
return height;
}

function makeMountains(count) {
const grid= {};

const size = 180;
const step = size / (count-1);
for (var z = 1; z < count-1; z++) {
const zz = -size/2 + size / count * z;
for (var x = 1; x < count-1; x++) {
const xx = -size/2 + size / count * x;
const h = Math.max(1, Math.min(count-1, heightField([xx, zz]) * count / 32));
for (var y=1; y<h; y++) {
for (var dz=-1; dz<=0; dz++) for (var dy=-1; dy<=0; dy++) for (var dx=-1; dx<=0; dx++) {
const key = (x+dx) + (y+dy) * count + (z+dz) * count * count;
if (!(key in grid)) grid[key] = 0;
grid[key] |= !(dx || dy || dz);
}
}
}
}

const model = modelFromGrid(grid, count);
return model;
}

function modelFromGrid(grid, grid_size) {
const model = silhouette.newModel();

Object.keys(grid).forEach(key => {
const x = key % grid_size;
const y = (key / grid_size | 0) % grid_size;
const z = key / grid_size / grid_size| 0;
const cx = (x - grid_size / 2);
const cy = (y - grid_size / 2);
const cz = (z - grid_size / 2);
if (render) {
const polys = getTriangles(grid, grid_size, x, y, z, [cx, cy, cz], 1/2);
} else {
if (grid[key]) {
const mdl = makeBox(1, 1, 1);
mdl.transform(new Matrix().translate(cx, cy, cz));
model.merge(mdl);
}
}
});

return model;
}

// http://paulbourke.net/geometry/polygonise/
const tri_table = [ [], [0, 8, 3], [0, 1, 9], [1, 8, 3, 9, 8, 1], [1, 2, 10], [0, 8, 3, 1, 2, 10], [9, 2, 10, 0, 2, 9], [2, 8, 3, 2, 10, 8, 10, 9, 8], [3, 11, 2], [0, 11, 2, 8, 11, 0], [1, 9, 0, 2, 3, 11], [1, 11, 2, 1, 9, 11, 9, 8, 11], [3, 10, 1, 11, 10, 3], [0, 10, 1, 0, 8, 10, 8, 11, 10], [3, 9, 0, 3, 11, 9, 11, 10, 9], [9, 8, 10, 10, 8, 11], [4, 7, 8], [4, 3, 0, 7, 3, 4], [0, 1, 9, 8, 4, 7], [4, 1, 9, 4, 7, 1, 7, 3, 1], [1, 2, 10, 8, 4, 7], [3, 4, 7, 3, 0, 4, 1, 2, 10], [9, 2, 10, 9, 0, 2, 8, 4, 7], [2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4], [8, 4, 7, 3, 11, 2], [11, 4, 7, 11, 2, 4, 2, 0, 4], [9, 0, 1, 8, 4, 7, 2, 3, 11], [4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1], [3, 10, 1, 3, 11, 10, 7, 8, 4], [1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4], [4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3], [4, 7, 11, 4, 11, 9, 9, 11, 10], [9, 5, 4], [9, 5, 4, 0, 8, 3], [0, 5, 4, 1, 5, 0], [8, 5, 4, 8, 3, 5, 3, 1, 5], [1, 2, 10, 9, 5, 4], [3, 0, 8, 1, 2, 10, 4, 9, 5], [5, 2, 10, 5, 4, 2, 4, 0, 2], [2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8], [9, 5, 4, 2, 3, 11], [0, 11, 2, 0, 8, 11, 4, 9, 5], [0, 5, 4, 0, 1, 5, 2, 3, 11], [2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5], [10, 3, 11, 10, 1, 3, 9, 5, 4], [4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10], [5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3], [5, 4, 8, 5, 8, 10, 10, 8, 11], [9, 7, 8, 5, 7, 9], [9, 3, 0, 9, 5, 3, 5, 7, 3], [0, 7, 8, 0, 1, 7, 1, 5, 7], [1, 5, 3, 3, 5, 7], [9, 7, 8, 9, 5, 7, 10, 1, 2], [10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3], [8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2], [2, 10, 5, 2, 5, 3, 3, 5, 7], [7, 9, 5, 7, 8, 9, 3, 11, 2], [9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11], [2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7], [11, 2, 1, 11, 1, 7, 7, 1, 5], [9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11], [5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0], [11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0], [11, 10, 5, 7, 11, 5], [10, 6, 5], [0, 8, 3, 5, 10, 6], [9, 0, 1, 5, 10, 6], [1, 8, 3, 1, 9, 8, 5, 10, 6], [1, 6, 5, 2, 6, 1], [1, 6, 5, 1, 2, 6, 3, 0, 8], [9, 6, 5, 9, 0, 6, 0, 2, 6], [5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8], [2, 3, 11, 10, 6, 5], [11, 0, 8, 11, 2, 0, 10, 6, 5], [0, 1, 9, 2, 3, 11, 5, 10, 6], [5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11], [6, 3, 11, 6, 5, 3, 5, 1, 3], [0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6], [3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9], [6, 5, 9, 6, 9, 11, 11, 9, 8], [5, 10, 6, 4, 7, 8], [4, 3, 0, 4, 7, 3, 6, 5, 10], [1, 9, 0, 5, 10, 6, 8, 4, 7], [10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4], [6, 1, 2, 6, 5, 1, 4, 7, 8], [1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7], [8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6], [7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9], [3, 11, 2, 7, 8, 4, 10, 6, 5], [5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11], [0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6], [9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6], [8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6], [5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11], [0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7], [6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9], [10, 4, 9, 6, 4, 10], [4, 10, 6, 4, 9, 10, 0, 8, 3], [10, 0, 1, 10, 6, 0, 6, 4, 0], [8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10], [1, 4, 9, 1, 2, 4, 2, 6, 4], [3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4], [0, 2, 4, 4, 2, 6], [8, 3, 2, 8, 2, 4, 4, 2, 6], [10, 4, 9, 10, 6, 4, 11, 2, 3], [0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6], [3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10], [6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1], [9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3], [8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1], [3, 11, 6, 3, 6, 0, 0, 6, 4], [6, 4, 8, 11, 6, 8], [7, 10, 6, 7, 8, 10, 8, 9, 10], [0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10], [10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0], [10, 6, 7, 10, 7, 1, 1, 7, 3], [1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7], [2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9], [7, 8, 0, 7, 0, 6, 6, 0, 2], [7, 3, 2, 6, 7, 2], [2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7], [2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7], [1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11], [11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1], [8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6], [0, 9, 1, 11, 6, 7], [7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0], [7, 11, 6], [7, 6, 11], [3, 0, 8, 11, 7, 6], [0, 1, 9, 11, 7, 6], [8, 1, 9, 8, 3, 1, 11, 7, 6], [10, 1, 2, 6, 11, 7], [1, 2, 10, 3, 0, 8, 6, 11, 7], [2, 9, 0, 2, 10, 9, 6, 11, 7], [6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8], [7, 2, 3, 6, 2, 7], [7, 0, 8, 7, 6, 0, 6, 2, 0], [2, 7, 6, 2, 3, 7, 0, 1, 9], [1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6], [10, 7, 6, 10, 1, 7, 1, 3, 7], [10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8], [0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7], [7, 6, 10, 7, 10, 8, 8, 10, 9], [6, 8, 4, 11, 8, 6], [3, 6, 11, 3, 0, 6, 0, 4, 6], [8, 6, 11, 8, 4, 6, 9, 0, 1], [9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6], [6, 8, 4, 6, 11, 8, 2, 10, 1], [1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6], [4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9], [10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3], [8, 2, 3, 8, 4, 2, 4, 6, 2], [0, 4, 2, 4, 6, 2], [1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8], [1, 9, 4, 1, 4, 2, 2, 4, 6], [8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1], [10, 1, 0, 10, 0, 6, 6, 0, 4], [4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3], [10, 9, 4, 6, 10, 4], [4, 9, 5, 7, 6, 11], [0, 8, 3, 4, 9, 5, 11, 7, 6], [5, 0, 1, 5, 4, 0, 7, 6, 11], [11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5], [9, 5, 4, 10, 1, 2, 7, 6, 11], [6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5], [7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2], [3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6], [7, 2, 3, 7, 6, 2, 5, 4, 9], [9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7], [3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0], [6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8], [9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7], [1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4], [4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10], [7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10], [6, 9, 5, 6, 11, 9, 11, 8, 9], [3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5], [0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11], [6, 11, 3, 6, 3, 5, 5, 3, 1], [1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6], [0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10], [11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5], [6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3], [5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2], [9, 5, 6, 9, 6, 0, 0, 6, 2], [1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8], [1, 5, 6, 2, 1, 6], [1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6], [10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0], [0, 3, 8, 5, 6, 10], [10, 5, 6], [11, 5, 10, 7, 5, 11], [11, 5, 10, 11, 7, 5, 8, 3, 0], [5, 11, 7, 5, 10, 11, 1, 9, 0], [10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1], [11, 1, 2, 11, 7, 1, 7, 5, 1], [0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11], [9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7], [7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2], [2, 5, 10, 2, 3, 5, 3, 7, 5], [8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5], [9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2], [9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2], [1, 3, 5, 3, 7, 5], [0, 8, 7, 0, 7, 1, 1, 7, 5], [9, 0, 3, 9, 3, 5, 5, 3, 7], [9, 8, 7, 5, 9, 7], [5, 8, 4, 5, 10, 8, 10, 11, 8], [5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0], [0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5], [10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4], [2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8], [0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11], [0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5], [9, 4, 5, 2, 11, 3], [2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4], [5, 10, 2, 5, 2, 4, 4, 2, 0], [3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9], [5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2], [8, 4, 5, 8, 5, 3, 3, 5, 1], [0, 4, 5, 1, 0, 5], [8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5], [9, 4, 5], [4, 11, 7, 4, 9, 11, 9, 10, 11], [0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11], [1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11], [3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4], [4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2], [9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3], [11, 7, 4, 11, 4, 2, 2, 4, 0], [11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4], [2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9], [9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7], [3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10], [1, 10, 2, 8, 7, 4], [4, 9, 1, 4, 1, 7, 7, 1, 3], [4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1], [4, 0, 3, 7, 4, 3], [4, 8, 7], [9, 10, 8, 10, 11, 8], [3, 0, 9, 3, 9, 11, 11, 9, 10], [0, 1, 10, 0, 10, 8, 8, 10, 11], [3, 1, 10, 11, 3, 10], [1, 2, 11, 1, 11, 9, 9, 11, 8], [3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9], [0, 2, 11, 8, 0, 11], [3, 2, 11], [2, 3, 8, 2, 8, 10, 10, 8, 9], [9, 10, 2, 0, 9, 2], [2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8], [1, 10, 2], [1, 3, 8, 9, 1, 8], [0, 9, 1], [0, 3, 8], [] ];
const edges = [ [0, 1], [1, 2], [2, 3], [3, 0], [4, 5], [5, 6], [6, 7], [7, 4], [4, 0], [5, 1], [6, 2], [7, 3] ];
const v_xyz = [ [-1, -1, -1], [1, -1, -1], [1, -1, 1], [-1, -1, 1], [-1, 1, -1], [1, 1, -1], [1, 1, 1], [-1, 1, 1] ];

function getTriangles(voxel_grid, grid_size, x, y, z, cxyz, r) {
var cube_index = 0;
for (var i=0; i<8; i++) {
const dx = v_xyz[i][0] * .5 + .5, dy = v_xyz[i][1] * .5 + .5, dz = v_xyz[i][2] * .5 + .5;
const idx = (x+dx) + (y+dy) * grid_size + (z+dz) * grid_size * grid_size;
if (idx in voxel_grid && voxel_grid[idx] == 1) {
cube_index |= 1 << i;
}
}
const polys = [];
var points = [];
tri_table[cube_index].forEach( (t, i) => {
const p0 = add3(mulf(v_xyz[edges[t][0]], r), cxyz);
const p1 = add3(mulf(v_xyz[edges[t][1]], r), cxyz);
const point = add3(p0, mulf(sub3(p1, p0), .5));
points.push(point);
if (((i+1)%3) == 0) {
polys.push(points);
points = [];
}
});
return polys;
}

function makeTower(ox, oy, oz, height, sides, radius, div) {
const astep = Math.PI * 2 / sides;
for (var i=0; i<sides * height; i++) {
const angle = i * astep;
const y = (i / sides | 0);

var matrix = new Matrix();
matrix.rotateY(Math.PI / 4);
matrix.rotateY(-angle + astep/2 * (y&1));
matrix.translate(ox, oy, oz);
const box = makeBox(1, 1, radius * div);
box.transform(matrix);
}
}

function makeWall(ox, oy, oz, rotY, width, height, brick_width, brick_height) {
for (var x=-width/2; x<width/2; x+=brick_width) {
for (var y=0; y<height; y+=brick_height) {
var matrix = new Matrix();
matrix.translate(ox, oy, oz);
matrix.translate(x + brick_width / 2 * ((y/brick_height|0)&1), y, 0);
matrix.rotateY(rotY);
const box = makeBox(brick_width, brick_height, 1);
box.transform(matrix);
}
}
}

function makeTorus(lr, lseg, cr, cseg, twist) {
const torus = silhouette.newModel();

const lstep = Math.PI * 2 / lseg;
const cstep = Math.PI * 2 / cseg;

for (var i=0; i<lseg; i++) {
const points = [];
for (var k=0; k<2; k++) {
points.push([]);
const a = (i + k) * lstep;
const cx = lr * Math.cos(a), cy = 0, cz = lr * Math.sin(a);
const matrix = new Matrix().rotateY(a).translate(cx, cy, cz);
for (var j=0; j<cseg; j++) {
const b = j * cstep + Math.PI / 4 + a * twist;
const point = matrix.transform([cr * Math.cos(b), cr * Math.sin(b), 0]);
points[k].push(point);
}
}

for (j=0; j<cseg; j++) {
torus.addFace([ points[0][j], points[0][(j+1)%cseg], points[1][(j+1)%cseg], points[1][j] ]);
}
}

}

function makePQTorus(p, q, lr, lseg, cr, cseg, twist, star) {
const torus = silhouette.newModel();

const lstep = Math.PI * 2 / lseg;
const cstep = Math.PI * 2 / cseg;

for (var i=0; i<lseg; i++) {
const points = [];
for (var k=0; k<2; k++) {
const a = (i + k) * lstep;
const r = lr * 0.5 * (2 + Math.sin(a * q));
const cx = r * Math.cos(a * p);
const cy = r * 0.5 * Math.cos(a * q);
const cz = r * Math.sin(a * p);

const matrix = new Matrix();
matrix.rotateY(a * p);
matrix.translate(cx, cy, cz);

points.push([]);
for (var j=0; j<cseg; j++) {
const b = j * cstep + Math.PI / 4 + a * twist;
const factor = 0.3 + (1 + Math.cos(a * p * 2)) * 0.5 * 0.7;
const r2 = cr * ((j&1) ? 1 : star) * factor;
const point = [
r2 * Math.cos(b),
r2 * Math.sin(b),
0
];
const tpoint = matrix.transform(point)
points[k].push(tpoint);
}
}

for (j=0; j<cseg; j++) {
const point00 = points[0][j];
const point01 = points[0][(j+1)%cseg];
const point10 = points[1][j];
const point11 = points[1][(j+1)%cseg];

const quad = [ point00, point01, point11, point10 ];
}
}

}

function project(op) {
const p = transform4([op[0], op[2], op[1], 1], viewProjectionMatrix);
const s = 5 * perspective **3;
if (p[2] < 0) return undefined;
return [ p[0]/p[3]*s, -p[1]/p[3]*s, p[2] ];
}

////////////////////////////////////////////////////////////////
// Polygon Clipping utility code - Created by Reinder Nijhoff 2019
// (Polygon binning by Lionel Lemarie 2021)
// https://turtletoy.net/turtle/a5befa1f8d
////////////////////////////////////////////////////////////////
function Polygons(){const t=[],s=25,e=Array.from({length:s**2},t=>[]),n=class{constructor(){this.cp=[],this.dp=[],this.aabb=[]}addPoints(...t){let s=1e5,e=-1e5,n=1e5,h=-1e5;(this.cp=[...this.cp,...t]).forEach(t=>{s=Math.min(s,t[0]),e=Math.max(e,t[0]),n=Math.min(n,t[1]),h=Math.max(h,t[1])}),this.aabb=[s,n,e,h]}addSegments(...t){t.forEach(t=>this.dp.push(t))}addOutline(){for(let t=0,s=this.cp.length;t<s;t++)this.dp.push(this.cp[t],this.cp[(t+1)%s])}draw(t){for(let s=0,e=this.dp.length;s<e;s+=2)t.jump(this.dp[s]),t.goto(this.dp[s+1])}addHatching(t,s){const e=new n;e.cp.push([-1e5,-1e5],[1e5,-1e5],[1e5,1e5],[-1e5,1e5]);const h=Math.sin(t)*s,o=Math.cos(t)*s,a=200*Math.sin(t),i=200*Math.cos(t);for(let t=.5;t<150/s;t++)e.dp.push([h*t+i,o*t-a],[h*t-i,o*t+a]),e.dp.push([-h*t+i,-o*t-a],[-h*t-i,-o*t+a]);e.boolean(this,!1),this.dp=[...this.dp,...e.dp]}inside(t){let s=0;for(let e=0,n=this.cp.length;e<n;e++)this.segment_intersect(t,[.1,-1e3],this.cp[e],this.cp[(e+1)%n])&&s++;return 1&s}boolean(t,s=!0){const e=[];for(let n=0,h=this.dp.length;n<h;n+=2){const h=this.dp[n],o=this.dp[n+1],a=[];for(let s=0,e=t.cp.length;s<e;s++){const n=this.segment_intersect(h,o,t.cp[s],t.cp[(s+1)%e]);!1!==n&&a.push(n)}if(0===a.length)s===!t.inside(h)&&e.push(h,o);else{a.push(h,o);const n=o[0]-h[0],i=o[1]-h[1];a.sort((t,s)=>(t[0]-h[0])*n+(t[1]-h[1])*i-(s[0]-h[0])*n-(s[1]-h[1])*i);for(let n=0;n<a.length-1;n++)(a[n][0]-a[n+1][0])**2+(a[n][1]-a[n+1][1])**2>=.001&&s===!t.inside([(a[n][0]+a[n+1][0])/2,(a[n][1]+a[n+1][1])/2])&&e.push(a[n],a[n+1])}}return(this.dp=e).length>0}segment_intersect(t,s,e,n){const h=(n[1]-e[1])*(s[0]-t[0])-(n[0]-e[0])*(s[1]-t[1]);if(0===h)return!1;const o=((n[0]-e[0])*(t[1]-e[1])-(n[1]-e[1])*(t[0]-e[0]))/h,a=((s[0]-t[0])*(t[1]-e[1])-(s[1]-t[1])*(t[0]-e[0]))/h;return o>=0&&o<=1&&a>=0&&a<=1&&[t[0]+o*(s[0]-t[0]),t[1]+o*(s[1]-t[1])]}};return{list:()=>t,create:()=>new n,draw:(n,h,o=!0)=>{reducedPolygonList=function(n){const h={},o=200/s;for(var a=0;a<s;a++){const c=a*o-100,r=[0,c,200,c+o];if(!(n[3]<r[1]||n[1]>r[3]))for(var i=0;i<s;i++){const c=i*o-100;r[0]=c,r[2]=c+o,n[0]>r[2]||n[2]<r[0]||e[i+a*s].forEach(s=>{const e=t[s];n[3]<e.aabb[1]||n[1]>e.aabb[3]||n[0]>e.aabb[2]||n[2]<e.aabb[0]||(h[s]=1)})}}return Array.from(Object.keys(h),s=>t[s])}(h.aabb);for(let t=0;t<reducedPolygonList.length&&h.boolean(reducedPolygonList[t]);t++);h.draw(n),o&&function(n){t.push(n);const h=t.length-1,o=200/s;e.forEach((t,e)=>{const a=e%s*o-100,i=(e/s|0)*o-100,c=[a,i,a+o,i+o];c[3]<n.aabb[1]||c[1]>n.aabb[3]||c[0]>n.aabb[2]||c[2]<n.aabb[0]||t.push(h)})}(h)}}}

////////////////////////////////////////////////////////////////
// Simplex Noise utility code. Created by Reinder Nijhoff 2020
// https://turtletoy.net/turtle/6e4e06d42e
// Based on: http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
////////////////////////////////////////////////////////////////
function SimplexNoise(t=1){const r=[[1,1,0],[-1,1,0],[1,-1,0],[-1,-1,0],[1,0,1],[-1,0,1],[1,0,-1],[-1,0,-1],[0,1,1],[0,-1,1],[0,1,-1],[0,-1,-1]],o=new Uint8Array(512),a=(Math.sqrt(3)-1)/2,n=(3-Math.sqrt(3))/6,s=(t,r)=>t[0]*r[0]+t[1]*r[1],h=(t,r)=>[t[0]-r[0],t[1]-r[1]];return new class{constructor(t=1){for(let t=0;t<512;t++)o[t]=255&t;for(let r=0;r<255;r++){const a=(t=this.hash(r+t))%(256-r)+r,n=o[r];o[r+256]=o[r]=o[a],o[a+256]=o[a]=n}}noise2D(t){const e=s(t,[a,a]),c=[Math.floor(t[0]+e),Math.floor(t[1]+e)],l=255&c[0],M=255&c[1],i=s(c,[n,n]),f=h(t,h(c,[i,i])),u=f[0]>f[1]?[1,0]:[0,1],m=h(h(f,u),[-n,-n]),x=h(f,[1-2*n,1-2*n]);let q=Math.max(0,.5-s(f,f))**4*s(r[o[l+o[M]]%12],f);return q+=Math.max(0,.5-s(m,m))**4*s(r[o[l+u[0]+o[M+u[1]]]%12],m),70*(q+=Math.max(0,.5-s(x,x))**4*s(r[o[l+1+o[M+1]]%12],x))}hash(t){const r=1103515245*((t=1103515245*(t>>1^t))^t>>3);return r^r>>16}}(t)}

// Random with seed
var rng;
function random() { if (rng === undefined) rng = new RNG(seed_t); return rng.nextFloat(); }
function RNG(t){return new class{constructor(t){this.m=2147483648,this.a=1103515245,this.c=12345,this.state=t||Math.floor(Math.random()*(this.m-1))}nextFloat(){return this.state=(this.a*this.state+this.c)%this.m,this.state/(this.m-1)}}(t)}

////////////////////////////////////////////////////////////////
// Projection from reinder's https://turtletoy.net/turtle/b3acf08303
let viewProjectionMatrix;
function setupCamera(t,e){const m=lookAt4m(t,e,[0,0,1]),n=perspective4m(.25,1);return multiply4m(n,m)}
function lookAt4m(o,n,r){const s=new Float32Array(16);n=normalize3(sub3(o,n)),r=normalize3(cross3(r,n));const t=normalize3(cross3(n,r));return s[0]=r[0],s[1]=t[0],s[2]=n[0],s[3]=0,s[4]=r[1],s[5]=t[1],s[6]=n[1],s[7]=0,s[8]=r[2],s[9]=t[2],s[10]=n[2],s[11]=0,s[12]=-(r[0]*o[0]+r[1]*o[1]+r[2]*o[2]),s[13]=-(t[0]*o[0]+t[1]*o[1]+t[2]*o[2]),s[14]=-(n[0]*o[0]+n[1]*o[1]+n[2]*o[2]),s[15]=1,s}
function perspective4m(t,n){const e=new Float32Array(16).fill(0,0);return e[5]=1/Math.tan(t/2),e[0]=e[5]/n,e[10]=e[11]=-1,e}
function multiply4m(t,r){const l=new Float32Array(16);for(let n=0;16>n;n+=4)for(let o=0;4>o;o++)l[n+o]=r[n+0]*t[0+o]+r[n+1]*t[4+o]+r[n+2]*t[8+o]+r[n+3]*t[12+o];return l}
function transform4(r,n){const t=new Float32Array(4);for(let o=0;4>o;o++)t[o]=n[o]*r[0]+n[o+4]*r[1]+n[o+8]*r[2]+n[o+12];return t}

function normalize3(a) { const len = len3(a); return scale3(a,len3<0.0001?1:1/len); }
function scale3(a,b) { return [a[0]*b,a[1]*b,a[2]*b]; }
function len3(a) { return Math.sqrt(dot3(a,a)); }
function add3(a,b) { return [a[0]+b[0],a[1]+b[1],a[2]+b[2]]; }
function sub3(a,b) { return [a[0]-b[0],a[1]-b[1],a[2]-b[2]]; }
function dot3(a,b) { return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]; }
function cross3(a,b) { return [a[1]*b[2]-a[2]*b[1],a[2]*b[0]-a[0]*b[2],a[0]*b[1]-a[1]*b[0]]; }
function mulf(v, f) { return [v[0]*f,v[1]*f,v[2]*f]; }